Bachmann said at a news conference that she had "no regrets" whatsoever, and said she ran her race with integrity and will continue to fight for the causes she emphasized on the campaign trail.
Former Massachusetts Gov. Mitt Romney won Tuesday night's contest, but just by eight votes over former Pennsylvania Sen. Rick Santorum. Texas Congressman Ron Paul took third place.
The race was so close that it was not until late in the night that it became clear that Romney was the winner. Romney had 30,015 votes, Santorum had 30,007 and Ron Paul scored 26,219 votes.
But while Romney gets to claim victory, Santorum clearly has the most momentum. He now heads to New Hampshire as the latest anybody-but-Romney Republican choice.
"Game on," Santorum declared.
Romney is also campaigning in New Hampshire, where he is expected to do well. He has been leading in the polls there for months.
He also got a big endorsement on Wednesday from Arizona Sen. John McCain, who ran against Romney in 2008.
Fellow GOP presidential hopeful Rick Perry is staying in the presidential race despite a fifth-place finish in the Iowa caucuses.
"And the next leg of the marathon is the Palmetto State...Here we come South Carolina!!!" he tweeted. The South Carolina primary is Jan. 21. New Hampshire's is next Tuesday.
As the Republicans turn up the heat, President Barack Obama tried to steal some of their thunder. He named Richard Cordray as the nation's chief consumer watchdog on Wednesday.
The Associated Press contributed to this report.